29,082 research outputs found
Analyticity of the density of electronic wavefunctions
We prove that the electronic densities of atomic and molecular eigenfunctions
are real analytic in away from the nuclei.Comment: 19 page
Many Particle Hardy-Inequalities
In this paper we prove three differenttypes of the so-called many-particle
Hardy inequalities. One of them is a "classical type" which is valid in any
dimesnion . The second type deals with two-dimensional magnetic
Dirichlet forms where every particle is supplied with a soplenoid. Finally we
show that Hardy inequalities for Fermions hold true in all dimensions.Comment: 20 page
Blockwise SVD with error in the operator and application to blind deconvolution
We consider linear inverse problems in a nonparametric statistical framework.
Both the signal and the operator are unknown and subject to error measurements.
We establish minimax rates of convergence under squared error loss when the
operator admits a blockwise singular value decomposition (blockwise SVD) and
the smoothness of the signal is measured in a Sobolev sense. We construct a
nonlinear procedure adapting simultaneously to the unknown smoothness of both
the signal and the operator and achieving the optimal rate of convergence to
within logarithmic terms. When the noise level in the operator is dominant, by
taking full advantage of the blockwise SVD property, we demonstrate that the
block SVD procedure overperforms classical methods based on Galerkin projection
or nonlinear wavelet thresholding. We subsequently apply our abstract framework
to the specific case of blind deconvolution on the torus and on the sphere
The electron density is smooth away from the nuclei
We prove that the electron densities of electronic eigenfunctions of atoms
and molecules are smooth away from the nuclei.Comment: 16 page
ANALYTIC STRUCTURE OF SOLUTIONS TO MULTICONFIGURATION EQUATIONS
Abstract. We study the regularity at the positions of the (fixed) nuclei of solutions to (non-relativistic) multiconfiguration equations (including Hartree–Fock) of Coulomb systems. We prove the following: Let {ϕ1,..., ϕM} be any solution to the rank–M multiconfiguration equations for a molecule with L fixed nuclei at R1,..., RL ∈ R 3. Then, for any j ∈ {1,..., M}, k ∈ {1,..., L}, there exists a neighbourhood Uj,k ⊆ R 3 of Rk, and functions ϕ (1) j,k, ϕ(2) j,k, real analytic in Uj,k, such that ϕj(x) = ϕ (1) (2) j,k (x) + |x − Rk|ϕ j,k (x), x ∈ Uj,k. A similar result holds for the corresponding electron density. The proof uses the Kustaanheimo–Stiefel transformation, as applied in [9] to the study of the eigenfunctions of the Schrödinger operator of atoms and molecules near two-particle coalescence points. 1. Introduction an
Einstein-Born-Infeld on Taub-NUT Spacetime in 2k+2 Dimensions
We wish to construct solutions of Taub-NUT spacetime in Einstein-Born-Infeld
gravity in even dimensions. Since Born-Infeld theory is a nonlinear
electrodynamics theory, in leads to nonlinear differential equations. However a
proper analytical solution was not obtain, we try to solve it numerically (by
the Runge-Kotta method) with initial conditions coinciding with those of our
previous work in Einstein-Maxwell gravity. We solve equations for 4, 6 and 8
dimensions and do data fitting by the least-squares method. For N=l=b=1, the
metric turns to the NUT solution only in 8 dimensions, but in 4 and 6
dimensions the spacetime does not have any Nut solution.Comment: 8 pages, 5 figure
Enhancement of perfluorooctanoate and perfluorooctanesulfonate activity at acoustic cavitation bubble interfaces
Acoustic cavitation driven by ultrasonic irradiation decomposes and mineralizes the recalcitrant perfluorinated surfactants perfluorooctanesulfonate (PFOS) and perfluorooctanoate (PFOA). Pyrolytic cleavage of the ionic headgroup is the rate-determining step. In this study, we examine the sonochemical adsorption of PFOX, where X = S for PFOS and A for PFOA, by determining kinetic order and absolute rates over an initial PFOX concentration range of 20 nM to 200 μM. Sonochemical PFOX kinetics transition from pseudo-first-order at low initial concentrations, [PFOX]_i 40 μM, as the bubble interface sites are saturated. At PFOX concentrations below 100 μM, concentration-dependent rates were modeled with Langmuir−Hinshelwood (LH) kinetics. Empirically determined rate maximums, V_(Max)^(−PFOA) = 2230 ± 560 nM min^−1 and V_(Max)^(−PFOS) = 230 ± 60 nM min^−1, were used in the LH model, and sonochemical surface activities were estimated to be K_(Sono)^(PFOS) = 120000 M^−1 and K_(Sono)^(PFOA) = 28500 M^−1, 60 and 80 times greater than equilibrium surface activities, K_(Eq)^(PFOS) and K_(Eq)^(PFOA). These results suggest enhanced sonochemical degradation rates for PFOX when the bubble interface is undersaturated. The present results are compared to previously reported sonochemical kinetics of nonvolatile surfactants
A new doubly discrete analogue of smoke ring flow and the real time simulation of fluid flow
Modelling incompressible ideal fluids as a finite collection of vortex
filaments is important in physics (super-fluidity, models for the onset of
turbulence) as well as for numerical algorithms used in computer graphics for
the real time simulation of smoke. Here we introduce a time-discrete evolution
equation for arbitrary closed polygons in 3-space that is a discretisation of
the localised induction approximation of filament motion. This discretisation
shares with its continuum limit the property that it is a completely integrable
system. We apply this polygon evolution to a significant improvement of the
numerical algorithms used in Computer Graphics.Comment: 15 pages, 3 figure
Spectral properties and geology of bright and dark material on dwarf planet Ceres
Variations and spatial distributions of bright and dark material on dwarf
planet Ceres play a key role in understanding the processes that have led to
its present surface composition. We define limits for bright and dark material
in order to distinguish them consistently, based on the reflectance of the
average surface using Dawn Framing Camera data. A systematic classification of
four types of bright material is presented based on their spectral properties,
composition, spatial distribution, and association with specific
geomorphological features. We found obvious correlations of reflectance with
spectral shape (slopes) and age; however, this is not unique throughout the
bright spots. Although impact features show generally more extreme reflectance
variations, several areas can only be understood in terms of inhomogeneous
distribution of composition as inferred from Dawn Visible and Infrared
Spectrometer data. Additional material with anomalous composition and spectral
properties are rare. The identification of the composition and origin of the
dark, particularly the darkest material, remains to be explored. The spectral
properties and the morphology of the dark sites suggest an endogenic origin,
but it is not clear whether they are more or less primitive surficial exposures
or excavated subsurface but localized material. The reflectance, spectral
properties, inferred composition, and geologic context collectively suggest
that the bright and dark material tends to gradually change toward the average
surface over time. This could be because of multiple processes, i.e., impact
gardening/space weathering, and lateral mixing, including thermal and aqueous
alteration, accompanied by changes in composition and physical properties such
as grain size, surface temperature, and porosity (compaction).Comment: Meteoritics and Planetary Science; Dawn at Ceres special issu
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